From (Model) Categories to Quasicategories

Related lectures (32)

Page 3 of 4

Explores lifting properties and model categories in topological spaces.

Covers the study of lifting properties in categories, focusing on the left and right lifting properties.

Introduces left and right derived functors in homotopical algebra, emphasizing their uniqueness and providing an illustrative example.

Introduces the homotopy category of a model category with inverted weak equivalences and unique homotopy equivalences.

Explains the construction of the homotopy category of a model category using cofibrant and fibrant replacement.

Introduces the course on homotopical algebra, exploring the power of analogy in pure mathematics.

Covers cylinders, path objects, and homotopy in model categories.

Covers two technical lemmas essential for the Fundamental Theorem in homotopical algebra.

Explores the characterization of fibrations and acyclic fibrations in chain complexes.

Explores the homotopy category of chain complexes and the relation between quasi-isomorphisms and chain homotopy equivalences.